Hausdorff Center for Mathematics Courses

Is There a Triangle Inequality for Measures of Compact, Convex Sets?

Explore geometric inequalities for convex bodies, focusing on surface area, Minkowski sums, and measure properties. Examine recent findings on monotonicity and supermodularity for Borel and Radon measures.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Query Lower Bounds for Log-Concave Sampling

Explores complexity lower bounds for sampling from log-concave distributions, using modified Perron's sprouting construction for Kakeya sets to establish tight bounds in low dimensions.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Isoperimetric Problem- From Classical to Reverse I

Explore the classical isoperimetric problem and its reverse, focusing on minimizing volume for convex bodies with bounded curvature. Learn about recent developments in R3.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Isoperimetric Problem- From Classical to Reverse II

Explore the reverse isoperimetric problem for convex bodies with bounded curvature, focusing on volume minimization in R3 and its implications for geometric analysis.

• YouTube
• 50 minutes
• On-Demand
• Free Video

The Floating Body Construction and Its Applications

Explore the floating body construction in geometry, its properties, and applications in affine surface area and random polytopes. Discover generalizations to non-Euclidean spaces.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Critical Intersection Volumes of -Schatten- P-Balls

Explores critical thresholds in high-dimensional geometry, focusing on intersection volumes of unit-volume balls and their limiting distributions, with applications to classical and Schatten p-balls.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Isoperimetric Problem - From Classical to Reverse III

Explores the reverse isoperimetric problem for convex bodies with bounded curvature, focusing on volume minimization in R3 and its implications for geometric analysis.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Clara Stegehuis- Optimization-Based Analysis of Random Graphs I

Explore random graph models, focusing on power-law degree distributions and optimization-based methods to analyze network properties and underlying geometries.

• YouTube
• 59 minutes
• On-Demand
• Free Video

David Steigenberger: Random Beta Simplices and Parallelotopes

Explore random simplices and parallelotopes in geometry, focusing on beta-distributed vectors. Learn about volume calculations and distributional representations using geometric approaches.

• YouTube
• 23 minutes
• On-Demand
• Free Video

Mean Distance in Polyhedra, an Application of the Crofton Reduction Technique

Explore the calculation of mean distances in polyhedra using the Crofton Reduction Technique, deriving exact forms for regular polyhedra beyond the cube.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Formalization in Homotopy Type Theory - Equivalences, 3-for-2 and Definitional Equality

Explore practical techniques for proving map equivalence in Homotopy Type Theory, focusing on the 3-for-2 property and definitional equality.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Formalizing Infinity-Category Theory in the Rzk Proof Assistant

Explore the formalization of ∞-category theory using the Rzk proof assistant, delving into advanced mathematical concepts and their computational representations.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Eye Tracking for Mathematics Research

Explore eye tracking technology's applications in mathematics education, research, and accessibility, uncovering insights into cognitive processes and learning strategies.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Proving an Execution of an Algorithm Correct - Ad Hoc UNSAT Verification

Explore algorithm correctness verification, focusing on cases where no solution exists. Learn about "ad hoc UNSAT verification" and its application in theorem proving.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Modularity in PVS

Explore modularity concepts in PVS theorem proving, enhancing code organization and reusability for complex formal verification projects.

• YouTube
• 35 minutes
• On-Demand
• Free Video